VOL. XXIX.] PHILOSOPHICAL TRANSACTIONS. • 247 



rate observation be had in both the places above-mentioned, it has already been 

 shown that the duration of these eclipses of Venus differ from each other by 17 

 entire minutes, on the supposition that the sun's parallax is 12^ seconds. And 

 if this difference be found to be greater or less by observation, the sun's parallax 

 will be greater or less nearly in the same ratio. And since 17 minutes of time 

 answer to 12-^ seconds of the sun's parallax; for each second of the parallax 

 there will arise a difference of upwards of 80 seconds of time; therefore, if 

 this difference be obtained true within 2 seconds of time, the quantity of the 

 sun's parallax will be got to within the 40th part of one second ; and conse- 

 quently his distance will be determined to within its 500th part; at least if the 

 parallax be not found less than what I have supposed it; for 40 X 12-i- is 500. 



Here I have had no regard to the planet's latitude, both to avoid the trouble 

 of a more intricate calculation, which would render the conclusion less evident, 

 as also on account of the motion of the nodes of Venus not being hitherto dis- 

 covered, and which can only be duly determined by such conjunctions of the 

 planet with the sun as this. For it was only on the supposition, that the plane 

 of Venus's orbit is immoveable in the sphere of the fixed stars, and that her 

 nodes would continue in the same places as they were in 1639, that it was con- 

 cluded, that Venus would pass 4 minutes below the sun's centre. But if in 1 76 1 

 she should pass more southerly, it will be evident, that there is a regression of 

 the nodes; and if more northerly, that there is a progression of them; and 

 that at the rate of 5-|- minutes in 100 Julian years, for each minute by which 

 the path of Venus will at that time be more or less distant from the sun's centre 

 than the said 4 minutes. But the difference between the durations of these 

 eclipses will be somewhat less than 1 7 minutes, by reason of the southern lati- 

 tude of Venus; but greater if, by the progression of the nodes, she shall pass 

 over the sun to the north of his centre. 



But for the sake of such as are not thoroughly acquainted with the doctrine 

 of parallaxes, I shall further explain the matter both by a figure and a somewhat 

 more accurate calculation. Therefore, supposing that at London, May 25, 

 17^ 55"^, 1761, the sun be in 15° 37' of Gemini, and consequently that at his 

 centre the ecliptic tends towards the north in an angle of 6° 10'; and that the 

 visible path of Venus within the sun's disk at that time descends towards the 

 south, forming an angle with the ecliptic of 8° 28'; then the path of Venus 

 will tend a little towards the south in respect of the equator, intersecting the 

 parallels of declination in an angle of 2° 18'. Supposing likewise that Venus be 

 near the sun's centre at the said time, and distant from it towards the south 4 

 minutes, describing, by a retrograde motion on the sun's disk, 4 minutes an 

 hour. The sun's semi-diameter will be nearly 15' 51'^, and that of Venus 37t''- 



